Two fuzzy if-then rules Jang, 1992 are given as follows:
Rule 1: If, x is A
1
and y is B
2
, then
1 1
1 1
f p x
q y r
5 Rule 2: If, x is A
2
and y is B
2
, then
2 2
2 2
f p x
q y r
6 Layer 1 Every adaptive node in this layer is a square
node with the node functions:
1,
, 1, 2
i
i A
O x i
7
2
1,
, 3, 4
i
i B
O y
i
8
where O
1,1
and O
1,2
are used to grade the memberships of fuzzy sets
A and B. Usually, a bell
function is used as follows:
2
1 ,
1, 2 1
i i
A b
i i
x i
x c
a
9
where a
i
, b
i
, and c
i
are the premise parameters.
Layer 2 Every adaptive node in this layer multiplies the incoming signal and sends the product out; the output is
determined by:
2,
, 1, 2
i i
i i
A B
O w
x y
i
10 Layer 3 Ratio of the rules for firing strength to the sum
of all rule ’s firing strengths is given as:
3, 1
2
, 1, 2
i i
i
w O
w i
w w
11 Layer 4 In this layer, every adaptive node is a square
node with the function:
4,
, 1, 2
i i
i i
i i
i
O w f
w p x q y
r i
12 where
i
p ,
i
q ,
i
r
are the design parameters.
Layer 5 Fixed node computes the overall output as the summation of all coming signals; the output is as
follows:
5,
, 1, 2
i i
i i
i i
i i
i
w f O
w f i
w
13
2.2.4 Local Correlation Maximization-Complementary Superiority
LCMCS
To develop an ideal prediction model, this paper tried to solve several issues such as whether the existing TN
estimation models were suitable for use with land that had subsided as a result of the excessive extraction of
various resources such as groundwater, oil and coal, how to reduce noise while retaining as much useful
information as possible, and how to realize the complementary superiority between PLS and ANFIS to
further improve the estimation accuracy of models. In facing the above issues, the LCMCS method was
proposed; the main steps are as follows:
1 Spectral transforms. Spectral transforms help to reduce the influence of noise; therefore, each REF was
mathematically manipulated into FDR, log1R and log[1R].
2 LCM analysis. To maximize the use of TN response information and eliminate the interference of
noisy data, OSP and OCC of the original and transformed spectrum were obtained by LCM de-noising
method, which had significant correlativity with TN content.
3 Complementary
superiority. OSP
and measured TN values were used in PLS analysis, and
several principal components were acquired. Then these principal components and the measured TN contents
were used in ANFIS analysis, and the LCMCS models were established.
4 Model-verifying. In this study, from the 280 samples in each treatment, 150 samples were used for
model calibration and the remaining 130 samples were used for model verification. Then, the best model was
selected as the final model using the LCMCS method. By carefully applying spectral transforms to wavelet,
correlation, PLS, and ANFIS analysis methods, the LCMCS method can effectively remove noise while
preserving the detail information, taking full advantage of useful spectral information and eliminating the
interference of noisy data, and the complementary superiority between PLS and ANFIS are realized.
2.2.5 Model Evaluation Standard
